三转动数控台运动学尺度综合

Kinematics and dimension synthesis of numerical control table with three rotational degrees of freedom

针对先进制造领域对转动台的需求,以一种三转动自由度数控台为对象,研究了该机构的奇异位形、工作空间与尺度综合。利用闭环矢量方程机构进行位置分析与速度分析,根据雅可比矩阵判断三转动数控台的奇异位形,考虑各支链的滑鞍行程、铰链转动约束及支链干涉等因素,分析了三转动数控台的工作空间,以三转动数控台的结构参数为设计变量,采用静力传递指标作为目标函数,辅以恰当的约束条件,利用序列二次规划算法对三转动数控台进行尺度综合。通过算例给出了优化设计结果与结论。

By taking a NC table with three rotational degrees of freedom as the object of study,the singularity,workspace and dimension synthesis were researched.The position and velocity analysis for NC table were processed by means of vector equation.The inverse,forward and combined singularities were identified based on the analysis of Jacobian matrix.The workspace of NC table was analyzed by considering the influencing factor of the saddle travel,the rotation range of joints and the interferences of linkages.By taking structure parameters of NC table taken as the design variables,the static transmission index as the objective function,some appropriate constraints and the sequential quadratic programming algorithm were applied to solve this nonlinear constrained optimization.The result of dimension synthesis and the conclusion were presented with an example.